FAYETTEVILLE, Ark. - To find out how cryptography, card tricks and kangaroos relate to one another, the curious may want to attend a lecture by Georgia Tech mathematician Michael Lacey, who will be speaking as part of a distinguished lecture series held on the University of Arkansas campus.

Researchers from all over the world will give lectures on some of the current issues in mathematics at the 27^th annual Arkansas Spring Lecture Series, held April 11-13 at the University of Arkansas Center for Continuing Education off the Fayetteville Square.

This year’s featured lecturer will be Michael Christ from the University of California-Berkeley. He and the other invited speakers will talk about harmonic analysis, multilinear operators and Schroedinger operators.

Mathematicians attempt to produce quantitative models that reflect real-life situations, said Luca Capogna, assistant professor of mathematics and co-organizer of this year’s lecture series. The better the model relates to what happens in the real world, the easier it is to use the model to make predictions about how changes will affect real-world situations.

Harmonic analysis, a way of representing a signal in terms of a combination of simple signals, is a modeling technique that has produced many successful applications, including the storage of sound information in digital form and the storage and recognition of digital fingerprints—a technique used by the FBI.

Although mathematicians have used harmonic analysis for almost 200 years, today’s researchers concern themselves with descriptions of real-life phenomena that include change, like stock market fluctuations, Capogna said. These models use differential equations that contain unknown variables that need to be solved for. Today mathematicians use multilinear operators to solve complex nonlinear equations.

"It’s almost everywhere in mathematics," Capogna said. In the past, number theory, combinatorial mathematics and partial differential equations were three separate fields, but harmonic analysis has tied the fields together, he said.

Schrodinger operators represent a special subset of such operators introduced by the physicist of the same name. These operators describe the equilibrium of a system and are used as a quantitative way to study the quantum mechanics of physical systems.

In its 27^th year, the Arkansas Spring Lecture Series brings an invited mathematician to campus to talk about a subject of his or her choice and allows that person to invite other speakers to come and talk about related topics.

"That guarantees freshness and the discussion of 'hot topics,’" Capogna said.

Other invited speakers include Georgia Tech’s Michael Lacey, Steve Hofmann of the University of Missouri, Columbia, Nets Katz of Washington University in St. Louis, Alexander Kiselev of the University of Chicago, Fedor Nazarov of Michigan State University, Wilhelm Schlag of CalTech, Andreas Seeger and Stephen Wainger of the University of Wisconsin, Madison, Gigliola Staffilani of Stanford University, and Christoph Thiele of UCLA.

Lacey’s public lecture, which is directed at undergraduate students, will be held at 4 p.m. Wednesday, April 10, in room 217 of the Science Building.

The conference is funded by the National Science Foundation, by the Fulbright College of Arts and Sciences and by the department of mathematics.

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